Minimum Time Visiting All Points

Statement

You are given an array of $n$ points with integer coordinates on a 2D plane, points, where $\text{points}[i] = [x_i, y_i]$. Your task is to determine the minimum time in seconds required to visit all the points in the given order.

Movement rules:

1. In one second, you can perform any one of the following:

   1. Move vertically by one unit.

   2. Move horizontally by one unit.

   3. Move diagonally (1 unit vertically and 1 unit horizontally in 1 second).

2. You must visit the points in the exact sequence listed in the array.

3. You may pass through points that appear later in the order, but they will not count as visits.

Constraints:

• points.length $= n$

• $1 \leq n \leq 10^2$

• points[i].length $= 2$

• $-10^3 \leq$ points[i][0], points[i][1] $\leq 10^3$

Examples